Propagation of single valued magnetic solitary waves in circularly polarized ferrites

Abstract

In this paper, we investigate the propagation of electromagnetic short wave in a polarized ferromagnetic insulator. We deal with the model equation derived by Kamdem et al. (2021 Phys. Scr. E 96 115206) from the Maxwell’s equations supplemented by the Landau-Lifshitz-Gilbert equation while taking into account complex conjugation using the perturbative method, describing the propagation of ultra-short waves in polarized ferrites, subject to damping and inhomogeneous exchange effects. We restrict our attention to the system free from inhomogeneous exchange effects and damping effects as well. By direct evaluations and inspired by previous results concerning the Kraenkel-Manna-Merle system, we show that the system is integrable, providing its associated Lax-pairs alongside with conservation law, governing the dynamics of wave moving in these media. Following the inverse scattering transform method, Soliton solutions of the system are obtained, which are single-valued modes that can propagate in the so-called media. One, two, three and four-soliton solutions are obtained. Generalization is made to obtain N-soliton solution to the so called complex Kraenkel-Manna-Merle system. We study the scattering properties of these short-wave solutions restricting our attention to two-, three- and four-soliton. We discuss their properties at large time scale providing phase shifts that are analytical expressions characterizing interaction processes and, we reveal some physical implications of the results obtained.